The GOES-R Solar Ultra-Violet Imager (SUVI) will provide space weather consumers with high spatial resolution, rapidly-updated, solar imaging in six narrow bands in the wavelength range from 94Å to 304Å. The SUVI Ground Processing Algorithm will produce calibrated SUVI images with the metadata necessary for the end user to determine the Heliographic coordinates of any image pixel given the spacecraft ephemeris, the position of the Solar Pointing Platform, and the Guide Telescope photodiode readings. One aspect of the Monitor Space Instruments Performance component of the Product Monitor software for the GOES-R series is to constantly check the accuracy of the SUVI pointing accuracy by independently determining the pixel location of the center of the solar disk. To do this we have developed a novel limb finding algorithm that can robustly find the center of the solar disk despite complicating factors such as the strongly wavelength dependent solar morphology and brightness, solar flares, and solar proton and cosmic ray induced detector noise. This presentation describes our Sun Centering Algorithm and demonstrates its effectiveness on a variety of SUVI proxy data.